In dealing with problems connected with gravity waves, scientists and engineers frequently find it necessary to make lengthy theoretical calculations involving such wave characteristics as wave height, wave length, period, and water depth. Several approximate theoretical expressions have been derived relating the above parameters. Airy, for instance, contributed a very valuable and complete theory for waves traveling over a horizontal bottom in any depth of water. Due to the simplicity of the Airy theory, it is frequently used by engineers. This theory, however, was developed for waves of very small heights and is inaccurate for waves of finite height. Stokes presented a similar solution for waves of finite height by use of trigonometric series. Using five terms in the series, this solution will extend the range covered by the Airy theory to waves of greater steepness. No attempt has been made in this paper to specify the range where the theory is applicable. The coefficients in these series are very complicated and for a numerical problem, the calculations become very tedious. Because of this difficulty, this theory would be very little used by engineers unless the value of the coefficient is presented in tabular form. The purpose of this paper is to present the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L.

This report attempts to answer basic question» regarding the feasibility of reproducing in an engineering model the surge phenomenon that at various times occurs in Monterey Harbor, California. To this end, a fairly extensive discussion is devoted to the wind and wave climate prevailing in and near Monterey Bay. Sea and swell data are summarized for the deep-water vicinity-area and for Monterey Bay itself, with particular reference to the southern portion, for the coast of which the distribution of refraction coefficient values is given for ordinary waves. Monterey Harbor tends to be quite well protected from the longer-period swells. Statistical data for the occurrence of long-period waves at three sensor positions in Monterey Harbor are examined and compared with similar-type data for Santa Cruz Harbor, at the northern extremity of Monterey Bay, and for Half Moon Bay Harbor (some 60 miles north of Monterey). Seasonal peculiarities are in evidence. Energy spectra for the long wave data are compared with earlier studies, of the Corps of Engineers (1949) and with the results of Residuation analyses made in this report. The oscillating characteristics of Monterey Bay are examined from several points of view. First, known analytic modes of oscillation of the water body in various semi-enclosed basins of simple geometrical shape are discussed. Application is made to Monterey Bay by likening it to the quadrant of a circular basin of either uniform depth or paraboloidal bottom slope. For greater exactitude numerical methods of calculating the oscillating properties of the bay are pursued. These start from the premise that a nodal condition tends to prevail across the mouth of the bay between Pinos and Santa Cruz Points. An improved Defant-Raichlcn numerical ''talweg" procedure gives the expected two-dimensional (vertical plane) modes of oscillation, while an improved Stoker numerical procedure yields the expected thrce-dimens : onal modes of oscillation of the bay. The computer programs for performing these calculations have been checked by applying them to special cases for which the analytic solutions are known. The three-dimensional modes for the bay reveal that the deep Monterey 1 canyon has a profound effect on the oscillating regime. The submerged , canyon causes the bay to function virtually as two independent halves about | the canyon centerline with only weak coupling between the two sections. 1 The three-dimensional numerical analysis, however, is considered to be reliable only for the lowest modes of oscillation because of the considerable uncertainty that the node-condition at the bay-mouth can be sustained for higher modes of oscillation of the bay. Because of this deficiency, the two-dimensional numerical procedure was applied to the Monterey bight (east of the Monterey Peninsula), and the modes of oscillation found for this smaller bay are expected to be more representative of the area enveloping the harbor. A detailed study is made of the manner of propagation of long period waves into Monterey Bay. Wav...

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Recent studies of the hydrodynamic responses of Los Angeles-Long Beach Harbors to the effects of long period waves [conducted in 1967-68 for the U.S. Army Corps of Engineers, Los Angeles District (35 )] , showed that the basins had characteristic modal periods of oscillation, which could be excited, apparently, on rather rare and largely unpredictable occasions. Available field data for confirmation of the mathematical results were largely non-existent at the time and satisfactory correlations were greatly hampered. In the interim the development of the Southeast Basin, Long Beach Harbor, for the reception of fast container ships has led to more detailed study and measurement of the responses of this particular basin to long period waves. The purpose of this paper is to present some of the original theoretical results of the 1968 study and examine their correlation with data of recent acquisition. Their bearing upon the motions in surge and sway of ships moored within the Southeast Basin will also be examined briefly in the light of some simple measurements of ship motions.

The "Bathystrophic Storm Tide Theory" is used to predict open-coast storm surge due to major hurricanes. The model described here is used to calculate storm-surge effects such as flood elevations needed for designing nuclear power plant safety related structures. In order to establish the model's viability the numerical techniques have been verified and the model calibrated using available field data. Numerical verification was performed for special cases where the governing equations of the model could be analytically solved. Inherent in the governing storm-tide equations are certain undetermined coefficients that describe the effects of wind drag and bottom friction. These coefficients were determined by correlating computer predicted results to hurricane storm surge hydrographs of record. As a result of this study, we find excellent agreement between computer predicted and analytical results.